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By Minoru Fujimoto
Section transitions within which crystalline solids suffer structural alterations current an attractive challenge within the interaction among the crystal constitution and the ordering method. this article, meant for readers with a few past wisdom of condensed-matter physics, emphasizes the fundamental physics at the back of such spontaneous structural alterations in crystals. beginning with the proper thermodynamic rules, the e-book discusses the character of order variables and their collective movement in a crystal lattice; in a structural part transition a singularity in one of these collective mode is liable for the lattice instability, as published by way of smooth phonons. This mechanism is similar to the interaction of a charge-density wave and a periodically deformed lattice in low-dimensional conductors. The textual content additionally describes experimental equipment for modulated crystal constructions and provides examples of structural adjustments in consultant structures. The e-book is split into elements. the 1st, theoretical, half comprises such themes as: the Landau concept of part transitions; data, correlations and the mean-field approximation; pseudospins and their collective modes; smooth lattice modes and pseudospin condensates; lattice imperfections and their function within the section transitions of genuine crystals. the second one half discusses experimental stories of modulated crystals utilizing x-ray diffraction, neutron inelastic scattering, mild scattering, dielectric measurements, and magnetic resonance spectroscopy.
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Extra info for The Physics of Structural Phase Transitions
Example text
Pseudospins in Displacive Crystals Among crystalline systems undergoing phase transitions, there is a group of crystals where the structural change is signified by active ions or molecules involved in continuous displacements. At the threshold of such transitions, these active groups begin to exhibit linear or rotational displacements in some cases and distortion in others, as evidenced by X-ray diffraction [19] and magnetic resonance results [20], [21]. Arising from continuous displacements, these so-called displacive phase transitions are second order according to the Ehrenfest classification, and characterized by a classical displacement vector signifying symmetry change at the transition temperatures.
Based on the classical model of pseudospins, the quartic potential is attributed to correlations only statistically, while it is clear in the quantum description that such correlations signifying the critical region is represented by a quartic term in the Landau expansion. 4. 4. Collective Pseudospin Modes in Displacive Systems For tunneling protons in a hydrogen-bonding crystal, their motion is involved in energy dissipation through the potential barrier, so that they are virtually independent, and their average positions are not significantly related by the periodicity of the lattice.
19) Although very unusual for first-order equil~bria, such a slow process as t ยป t o may occur in structural phase transitions of second order, as indicated by recent low-frequency experiments in the critical region, where tluctuations are in the range of microwave frequencies lower than 10- 10 Hz. ) Therefore, such a slow process is not entirely academic, but representing a realistic process in the critical region of secondorder phase transitions. Despite the presence of appreciable transition anomalies, the second-order phase transition is continuous theoretically.